Twin building lattices do not have asymptotic cut-points

TL;DR

This paper proves that twin building lattices exhibit linear divergence, leading to the conclusion that their asymptotic cones lack cut-points, which has implications for their geometric group theory properties.

Contribution

The paper establishes that twin building lattices have linear divergence, showing their asymptotic cones are without cut-points, a novel geometric property.

Findings

Twin building lattices have linear divergence.

Asymptotic cones of these lattices are without cut-points.

Implications for geometric group theory.

Abstract

We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.